2 Identifying Ice Floes and Computing Ice Floe Distributions in SAR Images
The chance of a pixel at (i,j) being an object at threshold slice 5, is
ct[(i,j) = object] = LConf(g(m,n),t(m,n)),
m,nEW(i,j)
15
where g(m,n) denotes the gray level at pixel (m,n), t(m,n) denotes the threshold of the
current slice at pixel (m,n), and Conf(a,b) is a step function that returns 0 if a 1 if a~b. To correlate the chances of a pixel at (i,j) of all threshold slices, we calculate the
sums as:
Cc(i,j) = LCt[(i,j) = object]
tEn,
Cs(i,j) = LCt[(i,j) = object]
tEn,
Finally, to label each pixel in the core or the skin image, we compare Cii,j) or Cs(i,j) to
a pre-specified threshold, Tc or Ts. These two thresholds were obtained experimentally to be Tc= 0.90 and Ts = 0.75. Every pixel in the image is an object pixel in the core
image if and only if Cc(i,j) is greater than Tc , and every pixel at (i,j) is an object pixel
in the skin image if and only if Cs(i,j) is greater than Ts.
2.3.3
Morphological Cleaning
Both core and skin images as presented in the previous discussion are noisy. To eliminate the noise effects while preserving the shape of the objects effectively, we use two
operators from mathematical morphology, dilation and erosion, which have been
employed to smooth contours and remove noise effects in various imagery, including
sea ice imagery (for example, Chou et al. 1994). The formal definitions of these two operators and extensions are provided in Matheron (1975) and Serra (1982).
- Dilation: The value of a pixel is replaced with the object class value if one of its 8neighbors is an object pixel; otherwise, it is set to nonobject. This is analogous to an
OR operation.
- Erosion: The value of a pixel is replaced with the object class value if all of its 8-neighbors are object pixels; otherwise, it is set to nonobject. This is analogous to an AND
operation.
- Opening: This is a combination of first erosion and then dilation on an image.
- Closing: This is a combination of first dilation and then erosion on an image.
We further define one complex operation as follows:
- Cleaning: This is a combination of first closing and then opening on an image.
The chance of a pixel at (i,j) being an object at threshold slice 5, is
ct[(i,j) = object] = LConf(g(m,n),t(m,n)),
m,nEW(i,j)
15
where g(m,n) denotes the gray level at pixel (m,n), t(m,n) denotes the threshold of the
current slice at pixel (m,n), and Conf(a,b) is a step function that returns 0 if a 1 if a~b. To correlate the chances of a pixel at (i,j) of all threshold slices, we calculate the
sums as:
Cc(i,j) = LCt[(i,j) = object]
tEn,
Cs(i,j) = LCt[(i,j) = object]
tEn,
Finally, to label each pixel in the core or the skin image, we compare Cii,j) or Cs(i,j) to
a pre-specified threshold, Tc or Ts. These two thresholds were obtained experimentally to be Tc= 0.90 and Ts = 0.75. Every pixel in the image is an object pixel in the core
image if and only if Cc(i,j) is greater than Tc , and every pixel at (i,j) is an object pixel
in the skin image if and only if Cs(i,j) is greater than Ts.
2.3.3
Morphological Cleaning
Both core and skin images as presented in the previous discussion are noisy. To eliminate the noise effects while preserving the shape of the objects effectively, we use two
operators from mathematical morphology, dilation and erosion, which have been
employed to smooth contours and remove noise effects in various imagery, including
sea ice imagery (for example, Chou et al. 1994). The formal definitions of these two operators and extensions are provided in Matheron (1975) and Serra (1982).
- Dilation: The value of a pixel is replaced with the object class value if one of its 8neighbors is an object pixel; otherwise, it is set to nonobject. This is analogous to an
OR operation.
- Erosion: The value of a pixel is replaced with the object class value if all of its 8-neighbors are object pixels; otherwise, it is set to nonobject. This is analogous to an AND
operation.
- Opening: This is a combination of first erosion and then dilation on an image.
- Closing: This is a combination of first dilation and then erosion on an image.
We further define one complex operation as follows:
- Cleaning: This is a combination of first closing and then opening on an image.